 Uniform material thinning under planar-sheet tension

For a thin planar viscous sheet with zero effective gravity and prescribed tensile force $F(t)$ per unit transverse width, force balance gives $4\mu h{w}_z=F(t)$. Conservation of mass gives $D_{t}h=-h{w}_z=-F/(4\mu )$, proving uniform subtraction from the initial material thickness. The material map satisfies $dz/d{z}_0=h_0/[h_0-\Delta ]$. Thus the same material thinning creates greater extension wherever the initial sheet is thinner.